1. Field of the Invention
The present invention relates generally to a system and a method for determining linear Stokes parameters and particularly to high-speed linear polarization imaging of a scene.
2. Background Art
There are several ways to describe the polarization of light. The polarization can be totally described by 4 parameters. There are many sets of 4 parameters that can be used. The most natural parameters are the Stokes parameters, which represent the intensity of the light, the amount of linearly polarized light, the orientation of the linear polarization, and the amount of circularly polarized light (with the sign of this parameter depending on the rotation of the light). The Stokes parameters are regrouped in the Stokes vector,
      S    =          (                                                  S              0                                                                          S              1                                                                          S              2                                                                          S              3                                          )        ,wherein S0 is the total intensity of the light, and S1=I0−I90 is the intensity of light through a horizontal polarizer minus the intensity of light through a vertical polarizer. For light that is totally linearly horizontally polarized, S1=S0, and for light that is totally vertically linearly polarized, S1=−S0.
Further, S2=I45−I−45 is the intensity of light that passed through a polarizer oriented at 45° minus the intensity of light that passed through a polarizer oriented at −45°. For light that is totally linearly polarized at 45°, S2=S0, and for light that is totally linearly polarized at −45°, S2=−S0. Finally, S3=Irh−IIh is the intensity of light that passed through a right-handed circular polarizer minus the intensity of light that passed through a left-handed circular polarizer. For light that is totally right-hand circularly polarized, S3=S0, and for light that is totally left-hand circularly polarized, S3=−S0.
The transformation of the Stokes vector of light propagating through an optical component can be described using the Mueller matrix of the component. Any optical component can be described by its Mueller matrix,
      S    out    =            (                                                  S              0              out                                                                          S              1              out                                                                          S              2              out                                                                          S              3              out                                          )        =                            M          comp                ⁢                  S          in                    =                        (                                                                      m                  11                                                                              m                  12                                                                              m                  13                                                                              m                  14                                                                                                      m                  21                                                                              m                  22                                                                              m                  23                                                                              m                  24                                                                                                      m                  31                                                                              m                  32                                                                              m                  33                                                                              m                  34                                                                                                      m                  41                                                                              m                  42                                                                              m                  43                                                                              m                  44                                                              )                ⁢                              (                                                                                S                    0                                          i                      ⁢                                                                                          ⁢                      n                                                                                                                                        S                    1                                          i                      ⁢                                                                                          ⁢                      n                                                                                                                                        S                    2                                          i                      ⁢                                                                                          ⁢                      n                                                                                                                                        S                    3                                          i                      ⁢                                                                                          ⁢                      n                                                                                            )                    .                    This linear algebra formalism is used to describe the change of polarization of light.
The linear Stokes parameters S0, S1, and S2 are the most used in polarization imaging as the circular polarization is not very common. Although it is possible to measure the linear Stokes parameters with only 3 polarization orientations (−60°, 0°, and 60° are generally used), these parameters are usually measured using 4 polarization orientations at −45°, 0°,45°, and 90°.
Currently, several systems for the measurement of linear Stokes parameters exist. One system includes a CCD camera with rotating polarizers. As an example, a rapid 4-Stokes parameter determination system comprising a filter wheel is described, for example, in U.S. Pat. No. 7,295,312. These systems can have a very good resolution. However, the mechanical rotation of a polarizer does not allow high speed measurements. This limits their use mainly to still targets and laboratory measurements.
Other systems use micropolarizer arrays in front of the sensor. These systems do not have moving parts so that they can be very fast. However, the achievable image resolution is reduced because of pixel interpolation to compensate for the fact that each pixel only sees one polarization state. The real lateral resolution of the final image is one half of the lateral resolution of the sensor due to the interpolation, leading to an effective reduction by a factor 4 the number of pixels of the sensor.
Finally, further systems include separated cameras that each see one state of polarization of the light. For example, document U.S. Pat. No. 5,557,324 discloses a polarization viewer with two CCD chips. Systems with separated cameras do not have moving parts, allow high resolution, but are very sensitive to alignment and also expensive as they require at least 3 times the hardware of a single camera.
It is an aim of the invention to provide an improved system and an improved method for polarization imaging and the determination of Stokes parameters.